The analysis of compact objects without spin up to the 1PN correction in the conservative orbital dynamics was reported in
[1]} for the first time using EFT techniques. Following this, the
2PN was computed in [2]}, [3]}, the 3PN was computed in [4]} and the 4PN was computed in [5]}, [6]}, [7]}, [8]}, [9]}. The current state of the art for the post-Newtonian calculation for the conservative potential is the 5PN correction computed in [10]}, [11]}. Several partial results of 6PN [12]}, [13]} have been recently added to the catalogue.
